1. Field of the Invention
The present invention relates to a distance measurement system accurately measuring a distance to an object under measurement with electromagnetic waves and an optical resolution improvement apparatus realizing, with quite high resolutions, measurement or observation of the profile of a surface condition or the surface condition of a cell, or the like by irradiation of laser lights, and is preferable for improving the resolution of an optical apparatus such as a microscope.
2. Description of the Related Art
With a conventional optical microscope, it has not been possible to observe or measure an object under measurement at or below a diffraction limit. As a substitute for this, a probe microscope (STM, AFM, NFOS, or the like), a scanning electron microscope, and so on have been developed and used in many fields. The scanning electron microscope uses a very narrow beam as a scanning electron probe, and thus has a high resolution and a significantly large focal depth as compared to the optical microscope. However, for measuring an object under measurement with low electric conductivity such as a cell, it is necessary to coat platinum palladium or gold with good electric conductivity on a sample as the object under measurement. Accordingly, this often accompanies damage to a cell itself, and of course it has not been possible to observe and measure a live cell.
Further, the probe microscope is to measure the distance to the object under measurement by making a probe, which is disposed close to the object under measurement, further close to the object under measurement, and utilizing atomic force, tunnel current, light near field or the like. However, it is difficult to move the probe at high speed, handling is difficult because the distance to the object under measurement is quite close, and moreover a long time is needed for obtaining two-dimensional information.
On the other hand, it is also conceivable to apply a system which irradiates an electromagnetic wave like a radar does, detects an electromagnetic wave from an object under measurement, and measures the distance to the object under measurement basically by a time difference between the time of transmission and the time of reception. However, in such a system, various signal processing algorithms are required and hence it is complicated, and also the size of the detectable object under measurement is limited.
On the other hand, for measuring a distance accurately or for measuring or observing a minute object accurately, heterodyne interference methods are well known. Here, an optical heterodyne method using lights will be described, but it is also performed with the similar idea for other electromagnetic waves. This optical heterodyne method makes two laser lights with different frequencies interfere with each other to create a beat signal of the frequency difference, and detects a phase change of this beat signal with a resolution of about 1/500 of a wavelength. That is, with this optical heterodyne method, it is possible to measure the distance to an object under measurement while measuring a change in height direction of a surface, or to measure or observe an object under measurement itself.
Then, Japanese Patent Application Laid-open No. S59-214706 of Patent Document 1 below discloses a method to adjacently generate two beams composed of different frequencies by using an acoustic optical device, detect a phase change between these two beams, and obtain a surface profile by increasing the phase change cumulatively. However, this Patent Document 1 is to make two beams be close and slightly larger than a beam profile, detect an average phase difference in two beam profiles by heterodyne wave detection, and sequentially integrate the phase difference, so as to obtain concave and convex information.
Therefore, according to this Patent Document 1, it is possible to measure concave and convex information of an object under measurement which is assumed to be flat such as a semiconductor wafer, but it is not possible to extract information inside the beam profile. Accordingly, it is not possible to increase the resolution inside the beam profile, which is in a plane.
On the other hand, a method called DPC (Differential Phase Contrast) method has been conventionally known. This is a technique applied first to an electron microscope by Dekkers and de Lang, and is thereafter expanded to an optical microscope by Sheppard and Wilson and others. This DPC method obtains a differential signal of results of interference between a zero order diffracted light and a first order diffracted light detected by detectors, which are in a far field with respect to electromagnetic waves irradiated to a sample and disposed symmetrically with respect to an irradiation axis of the electromagnetic waves, to thereby obtain profile information of the sample. However, when a spatial frequency increases, this DPC method is not able to make these zero order diffracted light and first order diffracted light interfere, and as a result of that the spatial frequency cannot be reproduced, the measurement can no longer be performed in some cases.
That is, including general apparatuses and the like using electromagnetic waves, conventional imaging-type microscopes using electromagnetic waves cannot exceed a resolution which is the limit of the Abbe's theory. This limit is a result of a diffraction phenomenon which a wave has, and has been assumed as a theological limit that cannot be exceeded. Therefore, it has been difficult to overcome the substantial limit by wavelengths used in not only the optical microscopes but also the electron microscopes.    Patent Document 1: Japanese Patent Application Laid-open No. 559-214706 (JP59214706(A))
As described above, in a conventional distance measurement apparatus using the heterodyne detection, it has not been possible to measure a distance with a resolution equal to or smaller than the wavelength of an electromagnetic wave to be given. Therefore, even when the irradiation area of the electromagnetic wave is decreased to be equal to or smaller than a wavelength, it has only been possible to calculate an average distance of an area to the extent equal to or larger than the wavelength.
Similarly, in a conventional optical detector using the heterodyne detection, a near-flat object such as a semiconductor wafer is a main target of measurement. Accordingly, to increase the resolution in a plane, it has been inevitable to use the near field of the electronic microscope, AFM (atomic force microscope), or the like.
However, regarding the electronic microscope, processing of a living organism, cell, or the like in particular is necessary, and thus live observation or measurement of a refractive-index distribution is not possible. On the other hand, the AFM has insufficient processing speed and hence is unable to see a change of state in real time. Thus, it is not suitable for observation of a living organism or cell, and meanwhile the probe needs to be close to the object under measurement, which causes poor usability.
Here, the OTF characteristics of an objective lens in a conventional microscope using an imaging optical system will be described below.
In the conventional microscope using an imaging optical system, the component of a first order diffracted light and the component of a zero order diffracted light of the spatial frequency of a target object, which is captured with the objective lens, interfere with each other to form an image. Accordingly, when the first order diffracted light is not incident on the aperture of the lens, the spatial frequency thereof would not be reproduced. On the other hand, the angle of diffraction of the first order diffracted light increases gradually as it varies from a low frequency to a high frequency, and hence the amount of the first order diffracted light inputted to the lens decreases progressively. As a result, the frequency whose first order diffracted light is not inputted is cut off, and the degree of modulation thereof gradually decreases in the course of variation from the low frequency to the high frequency.
The OTF characteristics of the objective lens are as described above. Therefore, in the imaging system, the first order diffracted light to be inputted to the objective lens is limited itself, and thus the resolution itself is has a limit in relation with the spatial frequency of the target object to be reproduced.
The above qualitative explanation is quantified and described in detail below.
As in FIG. 16, it is assumed that a parallel luminous flux is incident on an objective lens 31 having an aperture diameter a and a focal length f. Note that in FIG. 16, an irradiation optical axis is represented by an optical axis L0, and a tilted optical axis tilted by an angle Θ with respect to this optical axis L0 is represented by an optical axis L1. A microscope using normal imaging is a transmission type in which the luminous flux transmits a sample S as in FIG. 16, but it may be considered as a reflection type in which the luminous flux is returned by the sample S. Further, to make the equations simple, it is handled as a one-dimensional aperture.
Further, for simplicity, the sample S is assumed to be in the form of a sine wave with a height h and a pitch d. Specifically, an optical phase θ is represented by the following equation.θ=2π(h/λ)sin(2πx/d)  Equation (1)
The amplitude E of a light deflected from the sample S is given as a convolution of Fourier transform of Equation (1) and the aperture of the lens on a plane separated by the focal length f, and hence is represented as follows. However, the Bessel function which is Fourier transform of the phase of Equation (1) takes up to the positive and negative first order.
                                                        E              =                            ⁢                              ∫                                  (                                                                                                              J                          0                                                ⁡                                                  (                                                      2                            ⁢                            π                            ⁢                                                          h                              λ                                                                                )                                                                    ⁢                                              δ                        ⁡                                                  (                          X                          )                                                                                      +                                                                                                                                                          ⁢                                                                            J                      1                                        ⁡                                          (                                              2                        ⁢                        π                        ⁢                                                  h                          λ                                                                    )                                                        ⁢                                      (                                                                  δ                        ⁡                                                  (                                                      X                            -                                                                                          λ                                ⁢                                                                                                                                  ⁢                                f                                                            d                                                                                )                                                                    -                                              δ                        ⁡                                                  (                                                      X                            +                                                                                          λ                                ⁢                                                                                                                                  ⁢                                f                                                            d                                                                                )                                                                                      )                                                  )                            ⁢                              rect                ⁡                                  (                                                            x                      -                      X                                                              2                      ⁢                                                                                          ⁢                      a                                                        )                                            ⁢                              ⅆ                x                                                                                        =                            ⁢                                                                                          J                      0                                        ⁡                                          (                                              2                        ⁢                        π                        ⁢                                                  h                          λ                                                                    )                                                        ⁢                                      rect                    ⁡                                          (                                              x                                                  2                          ⁢                                                                                                          ⁢                          a                                                                    )                                                                      +                                                      J                    1                                    ⁡                                      (                                          2                      ⁢                      π                      ⁢                                              h                        λ                                                              )                                                                                                                                        ⁢                              (                                                      rect                    (                                                                  x                        -                                                                              λ                            ⁢                                                                                                                  ⁢                            f                                                    d                                                                                            2                        ⁢                                                                                                  ⁢                        a                                                              )                                    -                                      rect                    (                                                                  x                        +                                                                              λ                            ⁢                                                                                                                  ⁢                            f                                                    d                                                                                            2                        ⁢                                                                                                  ⁢                        a                                                              )                                                  )                                                                        Equation        ⁢                                  ⁢                  (          2          )                    
Here, the Fourier transform of Equation (2) contributes to imaging.
Therefore, intensity I is as following Equation (3)
                    I        =                                            (                                                                    J                    0                                    ⁡                                      (                                          2                      ⁢                      π                      ⁢                                              h                        λ                                                              )                                                  *                a                *                sin                ⁢                                                                  ⁢                                  c                  ⁡                                      (                    ka                    )                                                              )                        2                    +                      2            *                                          (                                                                            J                      1                                        ⁡                                          (                                              2                        ⁢                        π                        ⁢                                                  h                          λ                                                                    )                                                        *                                      (                                          a                      -                                                                        λ                          ⁢                                                                                                          ⁢                          f                                                                          2                          ⁢                                                                                                          ⁢                          d                                                                                      )                                    *                  sin                  ⁢                                                                          ⁢                                      c                    ⁡                                          (                                              k                        ⁡                                                  (                                                      a                            -                                                                                          λ                                ⁢                                                                                                                                  ⁢                                f                                                                                            2                                ⁢                                                                                                                                  ⁢                                d                                                                                                              )                                                                    )                                                                      )                            2                        *                          (                              4                ⁢                                                                  ⁢                                                      sin                    2                                    ⁡                                      (                                          2                      ⁢                      π                      ⁢                                              x                        d                                                              )                                                              )                                                          Equation        ⁢                                  ⁢                  (          3          )                    
What this equation means is that information of a pitch smaller than d=λf/2a=0.5λ/NA is dropped. This matches the beam diameter of a rectangular opening (the first dark ring diameter w of sin c(ka)=0 satisfies ka=π, and thus w=0.5×/NA). Further, this means that even when d>0.5λ/NA, the degree of modulation decreases as d becomes smaller. When the relation of this with the spatial frequency of 1/d and the degree of modulation is indicated, it is MTF.
As described above, in the ordinary imaging optical system, the limit of the spatial frequency reproduced by NA of the objective lens 31 is inevitably d=λf/2a=0.5λ/NA, and any value smaller than this would not be reproduced in any way.